Spatial aspects in the SMAD signaling pathway

Claus, Juliane; Friedmann, Elfriede; Klingmüller, Ursula; Rannacher, Rolf; Szekeres, Thomas

doi:10.1007/s00285-012-0574-1

Cited by 6 publications

(16 citation statements)

References 24 publications

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“…However, it is generally believed that cytokine signaling occurs in the regime of fast diffusion, which is reflected by our parameter values—the typical spatial range of fast diffusion, (see e.g. [ 55 ]), spans 40 cells away from the cytokine secreting cell for our values (see Table 1 ). Therefore, we analyzed the spatiotemporal dynamics of cytokine signals by more detailed mathematical modeling and simulations.…”

Section: Discussionmentioning

confidence: 99%

Three-Dimensional Gradients of Cytokine Signaling between T Cells

et al. 2015

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Immune responses are regulated by diffusible mediators, the cytokines, which act at sub-nanomolar concentrations. The spatial range of cytokine communication is a crucial, yet poorly understood, functional property. Both containment of cytokine action in narrow junctions between immune cells (immunological synapses) and global signaling throughout entire lymph nodes have been proposed, but the conditions under which they might occur are not clear. Here we analyze spatially three-dimensional reaction-diffusion models for the dynamics of cytokine signaling at two successive scales: in immunological synapses and in dense multicellular environments. For realistic parameter values, we observe local spatial gradients, with the cytokine concentration around secreting cells decaying sharply across only a few cell diameters. Focusing on the well-characterized T-cell cytokine interleukin-2, we show how cytokine secretion and competitive uptake determine this signaling range. Uptake is shaped locally by the geometry of the immunological synapse. However, even for narrow synapses, which favor intrasynaptic cytokine consumption, escape fluxes into the extrasynaptic space are expected to be substantial (≥20% of secretion). Hence paracrine signaling will generally extend beyond the synapse but can be limited to cellular microenvironments through uptake by target cells or strong competitors, such as regulatory T cells. By contrast, long-range cytokine signaling requires a high density of cytokine producers or weak consumption (e.g., by sparsely distributed target cells). Thus in a physiological setting, cytokine gradients between cells, and not bulk-phase concentrations, are crucial for cell-to-cell communication, emphasizing the need for spatially resolved data on cytokine signaling.

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Section: Discussionmentioning

confidence: 99%

Three-Dimensional Gradients of Cytokine Signaling between T Cells

et al. 2015

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“…The non-negativity of the concentrations is clearly essential in the term of biological interpretation. 6. Conclusion.…”

Section: Propositionmentioning

confidence: 95%

“…In Ref. [6] the authors investigate the SMAD signallig pathway. They compare the ODE model with the spatial model that assumes diffusion in the cytoplasm.…”

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confidence: 99%

Intracellular protein dynamics as a mathematical problem

Lachowicz¹,

Parisot²,

Szymańska³

2016

DCDS-B

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The present paper provides a mathematical analysis of the model of intracellular protein dynamics proposed in [14]. The model describes protein and mRNA transport inside a cell and takes into account diffusion in the nucleus and cytoplasm as well as active transport of protein molecules along microtubules in the cytoplasm. The model is a complex system of nonlinear PDEs with appropriate boundary conditions. The model reproduces, at least in numerical simulations, the oscillatory changes in protein concentration observed in the experimental data. To our knowledge this is the first paper that, in the multidimensional case, deals with a rigorous mathematical analysis of a model of intracellular dynamics with active transport on microtubules. In particular, in the present paper, we prove the existence and uniqueness result for the model in arbitrary space dimension. The model may be adapted to other signaling pathways.

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“…Incomplete list of such problems includes modeling of drug delivery to biological tissues [1], neural dynamics [2], mitochondrial swelling [3], intracellular signaling [4], cortical spreading depression [5], quantum information processing [6], active semiconductor media interacting with discrete elements [7], lumped circuits coupled to a transmission line [8], multiscale continuum mechanics [9].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov analysis of the spatially discrete-continuous system dynamics

Maksimenko

Hramov

Короновский

et al. 2017

Chaos, Solitons & Fractals

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Citation: MAXIMENKO, V.A. ... et al, 2017. Lyapunov analysis of the spatially discrete-continuous system dynamics. Chaos, Solitons and Fractals, 104, Additional Information:• This paper was accepted for publication in the journal Chaos, Soli- AbstractThe spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable andPreprint submitted to Elsevier August 31, 2017inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

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Spatial aspects in the SMAD signaling pathway

Cited by 6 publications

References 24 publications

Three-Dimensional Gradients of Cytokine Signaling between T Cells

Three-Dimensional Gradients of Cytokine Signaling between T Cells

Intracellular protein dynamics as a mathematical problem

Lyapunov analysis of the spatially discrete-continuous system dynamics

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